How to simulate the state-space model

Hello,

How to do the follow stace-space model in matlab or simulink. I only found the one input and output example.

thanks.

Answer 1

[Sam Chak]

Hi @Hein zaw

In MATLAB, you can use the ODE solver approach. If the system is LTI and you have the Control System Toolbox installed, you can also use the lsim() command. However, I generally advise students to learn the ODE solver approach because it provides a more versatile skill that can be applied to both linear and nonlinear state-space systems, avoiding the need to learn something new when dealing with the latter.

% Call ode45 solver
tspan   = linspace(0, 10, 1001);
x0      = [0, 0];
[t, x]  = ode45(@odefcn, tspan, x0);

% Pre-allocate for the system output signal y
y       = zeros(1, numel(t));

% Use for-loop to call odefcn() and compute y
for i = 1:numel(t)
    [~, y(i)] = odefcn(t(i), x(i,:).');
end

figure
plot(t, x, 'linewidth', 1.5), hold on
plot(t, y, 'linewidth', 1.5), hold off, grid on
xlabel('Time'), legend('x_1', 'x_2', 'y', 'location', 'best')

% Create a function that returns two outputs (math): dxdt and y
function [dxdt, y] = odefcn(t, x)
    % Inputs
    u1   = heaviside(t);
    u2   = 0.1*sin(2*pi/10*t);
    u    = [u1; 
            u2];
    
    % Matrix definitions
    A    = [ 0  1;      % state  matrix
            -2 -3];
    B    = [ 0  0;      % input  matrix
             1  1];
    C    = [ 3  1];     % output matrix
    D    = 0*C*B;       % direct matrix
    
    % State-space system
    dxdt = A*x + B*u;   % state  equation
    y    = C*x + D*u;   % output equation (system)
end

[Hein zaw]

Thank you, I will try.